Home Theater Noob Looking to Upgrade

Just for reference on the power handling of the speakers I am looking at:

RS-42 II x2 = 75W RMS/300W Peak
RB-51 II x2 = 75W RMS/300W Peak
RC-52 II x1 = 125W RMS/500W Peak

How do I need to interpret these numbers with respect to the ability of my AVR in powering these speakers?

Correct, too little power will burn out speakers a lot more than too much. Because all amps will generate more than their stated output of watts but with distortion. Its called driving the amplifier into "clipping" and it is this "clipped" power or distorted power that does the damage. Thats the THD figure you spoke about not being clear on - Total Harmonic Distortion. You want this number, relative to the watts, to be below 1%. So the lower the better.

Don't obsess about speaker power ratings. Its the sensitivity and impedence numbers that matter. The Klipsch are very sensitive at 96 db at 1 watt at 1 meter. This means that it will produce 96 db of sound pressure with only 1 watt at 1 meter away when fed a signal. Most of the time speakers are only operating on a couple of watts. Its only complex musical passages or high action scenes in movies where the speakers require more power to be delivered. And they are not all asking for it at the same time. This is why AVR manufacturers can boast big numbers from small power supplies into 5 or 7 speakers. Your Yamaha probably can deliver 85 wpc but only into ANY ONE SPEAKER at a time. And for brief moments when the speaker demands it. To deliver this amount into 5 speakers SIMULTANEOUSLY and CONTINUOUSLY, it probably falls off to 40-50 wpc. Still plenty to handle a set of Klipsch at 96 db efficiency.

If you like the Klipsch get them and don't worry. Also, after you get them, then consider upgrading your receiver to something with more power and your speakers will be ready. Just don't fall for the AVR marketing hype - look at manufacturers that are more honest with lower wattage ratings with ALL CHANNELS DRIVEN CONTINUOUSLY. This is why upper eschelon companies like NAD, Arcam, Cambridge Audio state far less power but at often 2-3 times the cost of a Yamaha. Its real, real power. Even the higher priced models from the mainstream AVR manufacturers like Yamaha will begin to get more honest at a certain price point. Learn to read the numbers! Hope all this helps - I am now at my personal 3 post limit in a thread LOL.

How big is your room ... Sound is about moving air in the end...

and how loud would you like your sound to be...
Movie theater loud..
WAF loud
etc..

You have been given good advice so far... you just need to match the numbers up to some context

The only other thing to look at on the receiver you have is whether it has 'Pre-Amp out' jacks. This is important for purposes of adding an amplifier to supplement the receiver's amps. I bought a receiver around Christmas and was assured it had the pre-amp outs to use my existing amp, and it turned out it didn't, so you have to look. I don't know the Yamaha line that well to know if it does. If, with the speakers you want, the receiver gets you all the volume you want without cranking the volume all the way, then you're all set - well, kinda - separate amps are always going to perform better, but sometimes the cost/benefit ratio isn't good.

Power ratings on speakers are next-to-useless. A low powered receiver working too hard will ALWAYS damage speakers before a 1000W brute amp.

This is amazing advice! Thank you all so much, and the AudiogoN Forum community for providing this platform. I may have some other questions about wiring, etc. but I will post them in the proper forums.